Method for determining optimum thickness measurement position, substrate processing method, and substrate processing apparatus

Abstract

Provided is a method for determining an optimum thickness measurement position when the thickness distribution of a substrate processed by a substrate processing apparatus is measured, the method including determining the optimum thickness measurement position on the basis of training data. The training data is acquired in advance by measuring a high-dimensional thickness distribution of one or more processed substrates. The optimum thickness measurement position to be determined is the thickness measurement position optimized on the basis of the training data so that, when estimation data that is a high-dimensional thickness distribution is calculated on the basis of actual measurement data acquired by measuring the thickness of the substrate at a certain thickness measurement position, the estimation data is close to the true high-dimensional thickness distribution.

Description

Method for determining optimum thickness measurement position, substrate processing method, and substrate processing apparatus

[0001] The present disclosure relates to a method for determining a thickness measurement position, a substrate processing method, and a substrate processing apparatus.

[0002] Patent Document 1 discloses that in measuring the thickness of a substrate, three points, namely, the center, the midpoint of the radius, and the outer periphery of the substrate, or five points, namely, the center, the midpoint of the radius, the midpoint between the center and the midpoint of the radius, and the midpoint between the midpoint of the radius and the outer periphery, are measured, and that an approximate straight line is derived from the thicknesses at the measurement points.

[0003] Japanese Patent Publication No. 2022-046137

[0004] The technology according to the present disclosure determines an optimized thickness measurement position when measuring the thickness distribution of a processed substrate during surface processing of the substrate.

[0005] One aspect of the present disclosure is a method for determining an optimal thickness measurement position when measuring the thickness distribution of a substrate processed in a substrate processing apparatus, the method including determining the optimal thickness measurement position based on training data, the training data being obtained in advance by measuring the high-dimensional thickness distribution of one or more of the processed substrates, and the optimal thickness measurement position to be determined is a thickness measurement position optimized based on the training data so that when estimated data, which is a high-dimensional thickness distribution, is calculated based on actual measurement data obtained by measuring the thickness of the substrate at a certain thickness measurement position, the estimated data is close to the true high-dimensional thickness distribution.

[0006] According to the present disclosure, in the surface processing of a substrate, an optimized thickness measurement position can be determined when measuring the thickness distribution of the processed substrate.

[0007] FIG. 1 is a plan view showing an outline of the configuration of a wafer processing system; FIG. 2 is a side view showing an outline of the configuration of an etching apparatus; FIG. 3 is an explanatory diagram showing how a nozzle moves in a radial direction; FIG. 4 is a side view showing an example of the configuration of a grinding unit and a chuck; FIG. 5 is an explanatory diagram showing how a wafer is ground; FIG. 6 is a flow chart showing main steps of wafer processing; FIG. 7 is a flow chart showing main steps of a method for determining optimal etching conditions; FIG. 8 is a flow chart showing main steps of a method for determining thickness measurement positions according to a first embodiment; and FIG. 9 is a flow chart showing main steps of a method for determining thickness measurement positions and a high-dimensional transformation matrix according to a second embodiment.

[0008] Hereinafter, a wafer processing system as a substrate processing system and a wafer processing method as a substrate processing method according to the present embodiment will be described with reference to the drawings. Note that in this specification and the drawings, elements having substantially the same functional configurations are designated by the same reference numerals, and redundant description will be omitted.

[0009] In a wafer processing system 1 serving as a substrate processing apparatus according to this embodiment, processing is performed on a wafer W serving as a substrate obtained by cutting from an ingot, in order to improve the in-plane thickness uniformity. Hereinafter, the cut surfaces of the wafer W will be referred to as a first surface Wa and a second surface Wb. The first surface Wa is the surface opposite the second surface Wb. The first surface Wa and the second surface Wb may also be collectively referred to as the surfaces of the wafer W.

[0010] 1, the wafer processing system 1 has a configuration in which a loading / unloading station 2 and a processing station 3 are integrally connected. In the loading / unloading station 2, for example, a cassette C capable of accommodating a plurality of wafers W is loaded and unloaded between the loading / unloading station 2 and the outside. The processing station 3 is equipped with various processing devices that perform desired processing on the wafers W.

[0011] The loading / unloading station 2 is provided with a cassette mounting table 10 on which a plurality of cassettes C, for example, three cassettes C, are mounted. A wafer transfer device 20 is provided adjacent to the cassette mounting table 10 on the negative side of the X-axis of the cassette mounting table 10. The wafer transfer device 20 is configured to be movable on a transfer path 21 extending in the Y-axis direction. The wafer transfer device 20 also has, for example, two transfer arms 22 that hold and transfer wafers W. Each transfer arm 22 is configured to be movable horizontally, vertically, around a horizontal axis, and around a vertical axis. The configuration of the transfer arms 22 is not limited to this embodiment and may have any configuration. The wafer transfer device 20 is configured to be able to transfer wafers W to the cassettes C on the cassette mounting table 10 and to a transition device 30, which will be described later.

[0012] In the loading / unloading station 2 , a transition device 30 for transferring the wafer W to and from the processing station 3 is provided adjacent to the wafer transfer device 20 on the negative side of the X axis of the wafer transfer device 20 .

[0013] For example, three processing blocks G1 to G3 are provided in the processing station 3. The first processing block G1, the second processing block G2, and the third processing block G3 are arranged in this order from the positive side of the X axis (the side of the loading / unloading station 2) to the negative side.

[0014] The first processing block G1 is provided with an etching device 40, a thickness measuring device 50, a reversing device 51, and a wafer transport device 60. The etching device 40, thickness measuring device 50, and reversing device 51 as an etching section are arranged in a stacked configuration. Note that the number and arrangement of the etching devices 40, thickness measuring devices 50, and reversing devices 51 are not limited to this.

[0015] The etching device 40 etches silicon (Si) on the first surface Wa or the second surface Wb after grinding by the grinding device 90 described below. In order to improve the throughput of wafer processing, a plurality of etching devices 40 may be provided.

[0016] As shown in FIG. 2, the etching device 40 includes a wafer holder 41 , a rotating mechanism 42 , a nozzle 43 , and a moving mechanism 44 .

[0017] The wafer holding unit 41 holds the outer edge of the wafer W at multiple points, three points in this embodiment. The configuration of the wafer holding unit 41 is not limited to the example shown in the figure, and for example, the wafer holding unit 41 may include a chuck (not shown) that suction-holds the wafer W from below. The wafer holding unit 41 is configured to be rotatable about a vertical rotation center line 41a by a rotation mechanism 42, thereby allowing the wafer W held on the wafer holding unit 41 to rotate.

[0018] The nozzle 43 supplies the etching liquid E to the first surface Wa or the second surface Wb of the wafer W held by the wafer holder 41. The nozzle 43 is connected to an etching liquid supply source (not shown) that supplies the etching liquid E to the nozzle 43. The nozzle 43 is provided above the wafer holder 41 and configured to be movable in the horizontal and vertical directions by a movement mechanism 44. In one example, the nozzle 43 is configured to be capable of reciprocating movement (scan movement) or swiveling along a rotation center line 41 a of the wafer holder 41, i.e., above the center of the wafer W as shown in FIG. 3 .

[0019] The etching solution E contains hydrofluoric acid (HF), nitric acid (HNO ３ ) and phosphoric acid (H ３ P.O. ４ In one example, the etching solution E is a mixed solution containing hydrofluoric acid, nitric acid, phosphoric acid, and water. The etching target may be, for example, amorphous silicon.

[0020] The thickness measurement device 50 shown in FIG. 1 includes, in one example, a measurement unit (not shown) and a calculation unit (not shown). The measurement unit includes a sensor that measures the thickness of the wafer W after etching at multiple points. The calculation unit acquires the thickness distribution of the wafer W from the measurement results (thickness of the wafer W) obtained by the measurement unit, and further calculates the thickness deviation (TTV: Total Thickness Variation) of the wafer W. The thickness deviation of the wafer W is the maximum value of the differences between the thickness of the target shape and the measured thickness. Note that the calculation of the thickness distribution and thickness deviation of the wafer W may be performed by the control device 150 described below instead of the calculation unit. In other words, a calculation unit (not shown) may be provided within the control device 150 described below. Note that the configuration of the thickness measurement device 50 is not limited to this and may be configured arbitrarily.

[0021] The reversing device 51 vertically reverses the first surface Wa and the second surface Wb of the wafer W. The reversing device 51 may have any configuration.

[0022] The wafer transfer device 60 is disposed on the negative side of the transition device 30 in the X-axis direction. The wafer transfer device 60 has, for example, two transfer arms 61 that hold and transfer a wafer W. Each transfer arm 61 is configured to be movable horizontally, vertically, around a horizontal axis, and around a vertical axis. The wafer transfer device 60 is configured to be able to transfer the wafer W to the transition device 30, the etching device 40, the thickness measurement device 50, the inversion device 51, the cleaning device 70 described below, the thickness measurement device 71 described below, the buffer device 72 described below, and the inversion device 73 described below.

[0023] The second processing block G2 is provided with a cleaning device 70, a thickness measuring device 71, a buffer device 72, an inverting device 73, and a wafer transfer device 80. The cleaning device 70, the thickness measuring device 71, the buffer device 72, and the inverting device 73 are arranged in a stacked configuration. Note that the number and arrangement of the cleaning devices 70, the thickness measuring devices 71, the buffer device 72, and the inverting device 73 are not limited to this.

[0024] The cleaning device 70 cleans at least the first surface Wa or the second surface Wb after grinding by the grinding device 90 described below.

[0025] In one example, the thickness measuring device 71 has the same configuration as the above-described thickness measuring device 50. However, the configuration of the thickness measuring device 71 is not limited to this, and can be configured arbitrarily.

[0026] The buffer device 72 temporarily holds unprocessed wafers W that are transferred from the first processing block G1 to the second processing block G2. The configuration of the buffer device 72 is optional. The buffer device 72 may also include an alignment mechanism (not shown) that adjusts the center position of the wafer W relative to chucks 93 a, 93 b (described later) and / or the horizontal orientation of the wafer W.

[0027] The reversing device 73 vertically reverses the first surface Wa and the second surface Wb of the wafer W. The reversing device 73 may have any configuration.

[0028] The wafer transfer device 80 is disposed, for example, on the Y-axis positive side of the cleaning device 70, the thickness measurement device 71, the buffer device 72, and the inverting device 73. The wafer transfer device 80 has, for example, two transfer arms 81 that suction-hold and transport the wafer W using a suction-holding surface (not shown). Each transfer arm 81 is supported by an articulated arm member 82 and is configured to be movable horizontally, vertically, around a horizontal axis, and around a vertical axis. The wafer transfer device 80 is configured to be able to transport the wafer W to the etching device 40, the thickness measurement device 50, the inverting device 51, the cleaning device 70, the thickness measurement device 71, the buffer device 72, the inverting device 73, and a grinding device 90, which will be described later.

[0029] The third processing block G3 is provided with a grinding device 90 as a grinding unit. The grinding device 90 grinds and flattens the first surface Wa or the second surface Wb of the wafer W.

[0030] The grinding device 90 has a rotary table 91. The rotary table 91 is configured to be rotatable about a vertical rotation center line 92 by a rotation mechanism (not shown). Four chucks 93a, 93b that suction-hold the wafer W are provided on the rotary table 91. Porous chucks, for example, are used as the chucks 93a, 93b. The surfaces of the chucks 93a, 93b, i.e., the holding surfaces for the wafer W, have a convex shape in which the central portion protrudes compared to the outer periphery in a side view. Note that although this protrusion in the central portion is minute, in the following description, the protrusion in the central portion of the chucks 93a, 93b may be illustrated exaggerated for clarity.

[0031] Of the four chucks 93a, 93b, two first chucks 93a are chucks used for grinding at a first processing position B1, which will be described later. These two first chucks 93a are arranged in positions that are point-symmetrical with respect to the rotation center line 92. The remaining two second chucks 93b are chucks used for grinding at a second processing position B2, which will be described later. These two second chucks 93b are also arranged in positions that are point-symmetrical with respect to the rotation center line 92. In other words, the first chucks 93a and the second chucks 93b are arranged alternately in the circumferential direction.

[0032] As shown in FIG. 4 , the four chucks 93a, 93b are respectively held by four chuck bases 94. The chuck base 94 is provided with a tilt adjustment mechanism 95 that adjusts the relative tilt between the grinding units 101, 111 (described later) and the chucks 93a, 93b. The tilt adjustment mechanism 95 has a fixed shaft 96 provided on the underside of the chuck base 94 and multiple, for example, two, lift shafts 97. Each lift shaft 97 is configured to be extendable and retractable, and raises and lowers the chuck base 94. The tilt adjustment mechanism 95 tilts the chucks 93a, 93b and the chuck base 94 by vertically raising and lowering the other end of the chuck base 94 using one end of the outer periphery of the chuck base 94 (a position corresponding to the fixed shaft 96) as a base point. This allows the relative tilt between the grinding surfaces of the grinding units 101, 111 at processing positions B1 to B2 (described later) and the upper surfaces of the chucks 93a, 93b to be adjusted. The configuration of the tilt adjustment mechanism 95 is not limited to this, and it is sufficient if it can adjust the relative angle (parallelism) of the surfaces (holding surfaces) of the chucks 93a and 93b with respect to the grinding surfaces of the grinding portions 101 and 111.

[0033] 1, the four chucks 93a, 93b can be moved to delivery positions A1-A2 and processing positions B1-B2 by rotating the rotary table 91. Furthermore, each of the four chucks 93a, 93b is configured to be rotatable about a vertical axis by a rotation mechanism (not shown).

[0034] The first transfer position A1 is a position on the positive X-axis side and the positive Y-axis side of the rotation center line 92 of the turntable 91, where the wafer W is transferred to the first chuck 93a when the first surface Wa is ground. The second transfer position A2 is a position on the positive X-axis side and the negative Y-axis side of the rotation center line 92 of the turntable 91, where the wafer W is transferred to the second chuck 93b when the second surface Wb is ground.

[0035] The first processing position B1 is a position on the negative X-axis side and the negative Y-axis side with respect to the rotation center line 92 of the rotary table 91, and the first grinding unit 100 is disposed therein. As an example, the first grinding unit 100 grinds the first surface Wa or the second surface Wb of the wafer W held by the first chuck 93 a.

[0036] As shown in FIG. 4 , the first grinding unit 100 has a grinding unit 101. The grinding unit 101 has a grinding stone 102, a grinding wheel 103, a mount 104, a spindle 105, and a drive unit 106. The grinding wheel 103 has an annular shape and supports the grinding stone 102 on its underside. The mount 104 supports the grinding wheel 103. The spindle 105 rotates the grinding wheel 103 and the grinding stone 102 via the mount 104. The drive unit 106 is attached to the spindle 105 and incorporates, for example, a motor (not shown), which rotates the spindle 105. As shown in FIG. 1 , the grinding unit 101 is configured to be movable vertically along a support 107 by a drive unit (not shown).

[0037] The second processing position B2 is a position on the negative X-axis side and the positive Y-axis side with respect to the rotation center line 92 of the rotary table 91, and the second grinding unit 110 is disposed therein. The second grinding unit 110 grinds, for example, the second surface Wb or the first surface Wa of the wafer W held by the second chuck 93b.

[0038] The second grinding unit 110 has the same configuration as the first grinding unit 100. That is, as shown in Figures 1 and 4, the second grinding unit 110 has a grinding section 111 (grinding stone 112, grinding wheel 113, mount 114, spindle 115, and drive section 116) and a support column 117.

[0039] As described above, the holding surfaces of the chucks 93a, 93b have a convex shape. Therefore, in the grinding process of the wafer W using the grinding units 100, 110, parts of the annular grinding wheels 102, 112 come into contact with the wafer W as processing points R, as shown by the bold lines in Fig. 5. More specifically, the annularly arranged grinding wheels 102, 112 contact the wafer W in an arc-shaped manner from the center to the outer peripheral edge. In this state, the entire surface of the wafer W is ground by rotating the chucks 93a, 93b and the grinding wheels 103, 113, respectively.

[0040] In addition, in the grinding units 100, 110, the tilt adjustment mechanism 95 described above adjusts the relative angle (tilt) between the holding surfaces of the chucks 93a, 93b and the grinding surfaces of the grinding wheels 102, 112, thereby controlling the shape of the wafer W after grinding to one of flat, convex (convex or A-shaped), concave (concave or V-shaped), W-shaped, and M-shaped, or a combination of any two of these. The flat shape is a shape in which the entire surface of the wafer W is adjusted to a desired thickness deviation (TTV) or less, preferably a shape in which the thickness is controlled to be uniform over the entire surface. The convex shape is a shape in which the thickness at the center of the wafer W is greater than the thickness at the outer periphery. The concave shape is a shape in which the thickness at the central recess of the wafer W is smaller than the thickness at the outer periphery. The W shape is a shape in which the thickness at the radial center of the wafer W is smaller than the thickness at the central and outer periphery. The M shape is a shape in which the thickness at the radial center of the wafer W is greater than the thickness at the central and outer periphery.

[0041] A thickness measuring device for measuring the thickness of the wafer W after grinding may be provided at the transfer positions A1, A2 or the processing positions B1, B2. In one embodiment, the thickness measuring device is configured to measure the thickness of the wafer W in the circumferential direction at a desired radial position of the wafer W while rotating the wafer W. In this case, the measuring unit of the thickness measuring device is configured to be movable corresponding to the desired radial position at which the thickness is to be measured. The radial position of the wafer W measured by the thickness measuring device includes, for example, a position near the center of the wafer W, near the outer periphery, or near the middle between the center and the outer periphery.

[0042] In one embodiment, the grinding apparatus 90 is provided with a display panel (not shown). The display panel is, for example, a monitor or a touch panel, and may be attached directly to the grinding apparatus 90 or may be a panel that can be viewed remotely. The display panel displays a screen for operating each process performed in the wafer processing system 1. A signal representing the operation result on the display panel is output to the control device 150, which will be described later.

[0043] In one embodiment, the different steps of the grinding process are not limited to the illustrated steps 1 to 3, but may include other steps as well. The different steps of the grinding process may include, for example, a step of lowering the grinding wheels 102, 112 relative to the wafer W until they come into contact with the wafer W, multiple steps of lowering the grinding wheels 102, 112 to a target position while changing the speed after they come into contact with the wafer W, a step of raising the grinding wheels 102, 112 from the target position to a position where they do not come into contact with the wafer W, and a step of raising the grinding wheels 102, 112 to a retracted position.

[0044] The wafer processing system 1 described above is provided with at least one control device 150 as a control unit, as shown in FIG. 1 . The control device 150 processes computer-executable instructions that cause the wafer processing system 1 to perform the various processes described in this disclosure. The control device 150 may be configured to control each element of the wafer processing system 1 to perform the various processes described herein. In one embodiment, some or all of the control device 150 may be included in the wafer processing system 1. The control device 150 is realized, for example, by a computer. The control device 150 may be one or more circuits, and may be provided as an integrated unit or partially separated. The control device 150 may include a processing unit, a memory unit, and a communication interface. The functions performed by the processing unit described in this disclosure may be implemented in circuitry or processing circuitry, including general-purpose processors, application-specific processors, integrated circuits, ASICs (Application Specific Integrated Circuits), CPUs (Central Processing Units), conventional circuitry, and / or combinations thereof, programmed to perform the described functions. A processor is considered to be a circuit or processing circuit including transistors and other circuitry. A processor may also be a programmed processor that executes a program stored in a memory unit. This program (computer program product) may be stored in a memory unit in advance or may be obtained via a medium H when needed. The medium H may be any of various computer-readable storage media, such as a removable storage medium such as a memory card, an optical disk, or a hard disk drive (HDD), and the program may be provided stored on the storage medium. The medium H may also be a communication line connected to the communication interface, and the program may be distributed by a remote server device or the like.The acquired program is stored in a storage unit and read from the storage unit and executed by a processing unit. The storage unit may include a storage medium such as a RAM (Random Access Memory), a ROM (Read Only Memory), an EEPROM (Electronically Erasable Programmable Read Only Memory), a HDD (Hard Disk Drive), or an SSD (Solid State Drive), or a combination thereof. The communication interface may communicate with the wafer processing system 1 via a communication line such as a LAN (Local Area Network). In this disclosure, a circuit, a unit, or a means is hardware programmed to realize the described function or hardware configured to execute the function. The hardware may be any hardware described in this disclosure or any hardware that is programmed to realize or known to perform the described functions. If the hardware is a processor that is considered to be a type of circuit, the circuit, means, or unit is a combination of hardware and software used to configure the hardware and / or processor.

[0045] <Wafer Processing Method> Next, a description will be given of a wafer processing method performed using the wafer processing system 1 configured as described above. In this embodiment, a process is performed on a wafer W cut from an ingot using a wire saw or the like, or a lapped wafer W, to obtain a desired thickness profile of the wafer W.

[0046] First, before processing the wafer W in the wafer processing system 1, the control device 150 determines a target thickness distribution (thickness profile) in the radial direction (within the wafer surface) when grinding the first surface Wa of the wafer W, which will be described later. Hereinafter, this target thickness distribution during grinding will be referred to as the "grinding target thickness distribution." The control device 150 also determines a target thickness distribution in the radial direction when grinding the second surface Wb of the wafer W, which will be described later (St1 in FIG. 6). Note that the method by which the control device 150 determines the grinding target thickness distribution of the first surface Wa and the grinding target thickness distribution of the second surface Wb will be described later.

[0047] Next, wafer processing is performed in the wafer processing system 1. In this wafer processing, first, a cassette C storing a plurality of wafers W is placed on the cassette mounting table 10 of the carry-in / out station 2. The wafers W are stored in the cassette C with their first surfaces Wa facing upward and their second surfaces Wb facing downward. Next, the wafer transfer device 20 removes the wafers W from the cassette C and transfers them to the transition device 30. The wafers W transferred to the transition device 30 are then transferred to the buffer device 72 by the wafer transfer device 60.

[0048] Next, the wafer W is transferred to the grinding device 90 by the wafer transfer device 80 and transferred to the first chuck 93a at the first transfer position A1. The second surface Wb of the wafer W is held by suction in the first chuck 93a.

[0049] Next, the turntable 91 is rotated to move the wafer W to the first processing position B1. Then, the first surface Wa is ground by the first grinding unit 100 based on the target grinding thickness distribution of the first surface Wa determined in St1 (St2 in FIG. 6). During grinding, grinding auxiliary water may be supplied to the first surface Wa of the wafer W from a nozzle (not shown) at a desired radial position and flow rate.

[0050] Next, the rotary table 91 is rotated to move the wafer W to the first delivery position A1.

[0051] Next, the wafer W is transferred to the cleaning device 70 by the wafer transfer device 80. In the cleaning device 70, the first surface Wa of the wafer W is cleaned (St3 in FIG. 6). In St3, the second surface Wb of the wafer W may also be cleaned.

[0052] Next, the wafer W is transferred to the reversing device 73 by the wafer transfer device 80. In the reversing device 73, the first surface Wa and the second surface Wb of the wafer W are reversed upside down (St4 in FIG. 6). That is, the wafer W is reversed so that the first surface Wa faces downward and the second surface Wb faces upward.

[0053] Next, the wafer W is transferred to the grinding device 90 by the wafer transfer device 80 and transferred to the second chuck 93b at the second transfer position A2. The first surface Wa of the wafer W is held by suction on the second chuck 93b.

[0054] Next, the turntable 91 is rotated to move the wafer W to the second processing position B2. Then, the second surface Wb of the wafer W is ground by the second grinding unit 110 based on the target grinding thickness distribution of the second surface Wb determined in St1 (St5 in FIG. 6).

[0055] Next, the rotary table 91 is rotated to move the wafer W to the second delivery position A2.

[0056] Next, the wafer W is transferred to the cleaning device 70 by the wafer transfer device 80. In the cleaning device 70, the second surface Wb of the wafer W is cleaned (St6 in FIG. 6). In St6, the first surface Wa of the wafer W may also be cleaned.

[0057] Next, the wafer W is transferred to the thickness measurement device 71 by the wafer transfer device 80 or the wafer transfer device 60. In the thickness measurement device 71, the thickness of the wafer W after grinding the second surface Wb is measured at multiple measurement positions (hereinafter referred to as "thickness measurement positions"). In one embodiment, a certain radial position between the center and outer circumferential edge of the wafer W is defined as one thickness measurement position. A sensor is then oriented at the thickness measurement position, and the wafer W is rotated in place to perform measurement, thereby performing circumferential measurement at the thickness measurement position. The measurement result is the circumferential thickness distribution of the wafer W at the thickness measurement position. The median or average of the circumferential thickness distribution is defined as the thickness data at the thickness measurement position. Note that in this embodiment, the radial position is defined by the radial distance from the center to the outer circumferential edge of the wafer W. However, in another embodiment, the radial position may be defined by the diameter distance from a certain outer circumferential edge position to another outer circumferential edge position on the opposite side of the center. Furthermore, in this embodiment, the entire circumferential circumference at a certain radial position is defined as one thickness measurement position, but this is not limited thereto. In another embodiment, a specific position on the surface of the wafer W is defined as one thickness measurement position, and the thickness at the specific position may be defined as the thickness data at the thickness measurement position. In this case, the specific position may be a single point on the surface of the wafer W, or multiple points that are in a desired relationship within the surface. If the specific positions are multiple points, the average value of the thicknesses at the specific positions may be defined as the thickness data at the thickness measurement position defined by the desired relationship.

[0058] The specific thickness measurement position is determined in advance as an optimal thickness measurement position by the methods according to the first to third embodiments described below. A thickness distribution (hereinafter referred to as "actual measurement data") is obtained by measuring at the optimal thickness measurement position. Furthermore, a high-dimensional thickness distribution (hereinafter referred to as "estimated data") of the wafer W estimated based on the actual measurement data is calculated (St7 in FIG. 6). In one embodiment, a thickness deviation of the wafer W is further calculated. The estimated data of the wafer W is calculated by the methods according to the first to third embodiments described below. The calculated thickness distribution and thickness deviation of the wafer W are output to, for example, the control device 150.

[0059] In one embodiment, the thickness of the wafer W during or after grinding is measured by a thickness measuring device (not shown) provided in the grinding apparatus 90. As an example, during grinding, i.e., while the grinding wheel is in contact with the wafer W and grinding is progressing, the thickness of the wafer W is measured in the circumferential direction at a position near the middle between the center and the outer circumferential edge, to obtain the progress of grinding in real time. Furthermore, after grinding, i.e., after the grinding wheel has separated from the wafer W, the thickness of the wafer W is measured at positions near the center, near the outer circumferential edge, and near the middle between the center and the outer circumferential edge, to obtain the overall thickness distribution of the wafer W. In one embodiment, the thickness of the wafer W during or after grinding measured by the thickness measuring device provided in the grinding apparatus 90 is output to, for example, the control device 150. In one embodiment, based on the thickness distribution of the wafer W output to the control device 150, grinding of the wafer W to be subsequently processed in the grinding apparatus 90 is optimized.

[0060] The control device 150 determines optimal etching conditions for the second surface Wb, which optimize the etching amount distribution (etching profile) in the etching process of the second surface Wb, from the estimated data of the thickness distribution of the wafer W and the thickness deviation calculated in St7 and output to the control device 150 (St8 in FIG. 6 ). Note that the etching amount is the amount of the wafer W removed by etching, and the etching amount distribution is the distribution of the etching amount in the radial direction (within the wafer surface) of the wafer W. The method for determining the optimal etching conditions for the second surface Wb in the control device 150 will be described later.

[0061] Next, the wafer W is transferred by the wafer transfer device 60 to the etching device 40. In the etching device 40, the second surface Wb of the wafer W is etched with the etching solution E under the optimal etching conditions determined in St8 (St9 in FIG. 6). In St9, the second surface Wb is etched under the optimal etching conditions, thereby processing the second surface Wb into a target shape.

[0062] Next, the wafer W is transferred to the reversing device 51 by the wafer transfer device 60. In the reversing device 51, the first surface Wa and the second surface Wb of the wafer W are reversed upside down (St10 in FIG. 6). That is, the wafer W is reversed so that the first surface Wa faces upward and the second surface Wb faces downward.

[0063] Next, the wafer W is transferred by the wafer transfer device 60 to the thickness measurement device 50. In the thickness measurement device 50, the thickness of the wafer W after etching the second surface Wb is measured at the optimal thickness measurement position, similar to St7 in the thickness measurement device 71. As a result, actual measurement data of the thickness distribution of the wafer W is obtained, estimated data is calculated, and further, a thickness deviation of the wafer W is calculated (St11 in FIG. 6 ). The calculated estimated data of the thickness distribution of the wafer W and the thickness deviation are output to, for example, the control device 150.

[0064] The control device 150 determines optimal etching conditions for the first surface Wa, which optimize the etching amount distribution in the etching process on the first surface Wa, from the estimated data of the thickness distribution of the wafer W and the thickness deviation calculated in St11 and output to the control device 150 (St12 in FIG. 6 ). The method for determining the optimal etching conditions for the first surface Wa in the control device 150 will be described later.

[0065] Next, the wafer W is transferred by the wafer transfer device 60 to the etching device 40. In the etching device 40, the first surface Wa of the wafer W is etched with the etching solution E under the optimal etching conditions determined in St12 (St13 in FIG. 6 ). In St13, by etching the first surface Wa under the optimal etching conditions, the etching amount distribution is optimized and the first surface Wa is processed into a target shape.

[0066] Next, the wafer W is transferred by the wafer transfer device 60 to the thickness measurement device 50. The thickness measurement device 50 measures the thickness of the wafer W after etching at multiple points on both the first surface Wa and the second surface Wb, thereby obtaining a thickness distribution of the wafer W (St14 in FIG. 6 ). The thickness measurement device 50 may further calculate a thickness deviation of the wafer W. In one embodiment, similar to St7 or St11, the thickness of the wafer W after etching is measured at an optimal thickness measurement position. In this manner, actual measurement data of the thickness distribution of the wafer W may be obtained, estimated data may be calculated, and the thickness deviation of the wafer W may further be calculated. The obtained estimated data of the thickness distribution and thickness deviation of the wafer W are output to, for example, the control device 150, and, for example, used for processing another wafer W to be processed next in the wafer processing system 1.

[0067] Thereafter, the wafer W that has been subjected to all the processes is transferred to the cassette C on the cassette mounting table 10 via the transition device 30. In this way, a series of wafer processes in the wafer processing system 1 is completed.

[0068] In the above embodiment, the first surface Wa is ground in St 2 and then the second surface Wb is ground in St 5, but the order of grinding these surfaces may be reversed. Also, the second surface Wb is etched in St 9 and then the first surface Wa is etched in St 13, but the order of etching these surfaces may be reversed.

[0069] Furthermore, in the above embodiment, etching of the second surface Wb in St9 was performed under the optimal etching conditions determined in St8, but instead, etching may be performed under predetermined default etching conditions. In such a case, Sts7 and St8 of this embodiment are omitted. Similarly, etching of the first surface Wa in St13 was performed under the optimal etching conditions determined in St12, but instead, etching may be performed under predetermined default etching conditions. In such a case, Sts11 and St12 of this embodiment are omitted.

[0070] Next, the method for determining the above-mentioned optimal etching conditions (Steps 8 and 12 in FIG. 6) will be described. In the following description, the method for determining the optimal etching conditions for the first surface Wa in Step 12 will be described, but the method for determining the optimal etching conditions for the second surface Wb in Step 8 is similar.

[0071] First, before processing the wafer W in the wafer processing system 1, a plurality of learning data are acquired (St100 in FIG. 7). The learning data is an etching amount distribution of the wafer W under certain etching conditions. The plurality of learning data is used to determine optimal etching conditions, as will be described later, and is also used to determine a target grinding thickness distribution, as will be described later.

[0072] In St100, etching is performed on a dummy wafer under, for example, a plurality of different etching conditions. Specifically, the dummy wafer is etched by changing, for example, the rotation speed R (also referred to as the number of rotations) of the dummy wafer during etching, the scanning speed V (also referred to as the swing speed) of the nozzle 43, the scanning width L (see the scanning width L in FIG. 3 , also referred to as the swing radius) of the nozzle 43, or the number of loops N of the nozzle 43. In this case, the etching processing time for each dummy wafer is the same. Similar to the etching in St13, the dummy wafer is etched by rotating the dummy wafer and supplying etching solution E from the nozzle 43 to the dummy wafer while the nozzle 43 is reciprocating. In the following description, the reciprocating movement of the nozzle 43 between both ends of the dummy wafer is considered to be one loop.

[0073] Etching of the dummy wafer under each etching condition is carried out for a predetermined desired time (desired number of loops). Then, the etching amount distribution of the dummy wafer is acquired and output to the control device 150. Furthermore, the control device 150 compresses the output etching amount distribution under each etching condition into an etching amount distribution per unit time (unit number of loops), and stores each compressed etching amount distribution as the learning data.

[0074] Although the above description has been given taking the example of acquiring the learning data by etching a dummy wafer as an example, the etching target when acquiring the learning data is not limited to a dummy wafer. Specifically, for example, the etching process results of a product wafer W processed in the wafer processing system 1 may be stored as the learning data. Furthermore, for example, if a film is formed on the first surface Wa of the wafer W, the etching target may be the film, and the etching process results of the film may be stored as the learning data.

[0075] Furthermore, although the learning data is acquired in the wafer processing system 1, it may be acquired outside the wafer processing system 1. In such a case, the control device 150 determines the optimal etching conditions based on the plurality of learning data acquired outside the wafer processing system 1.

[0076] Next, a target etching amount distribution for the etching process in St 13 is obtained based on the thickness distribution in the target shape of the wafer W after etching and the estimated data of the thickness distribution of the wafer W after grinding obtained in St 11 (St 110 in FIG. 7 ). The target etching amount distribution for the etching process can be obtained, for example, by calculating the difference between the thickness distribution in the target shape of the wafer W and the estimated data.

[0077] Next, multiple pieces of learning data (etching amount distributions) are superimposed, and an optimization method is used to optimize the learning data used for superimposition and the number of times the learning data is superimposed (St111 in FIG. 7 ) so that the target etching amount distribution obtained in St110 is obtained.

[0078] In St111, for example, the control of the etching amount distribution is applied to a knapsack problem to optimize the number of times that the learning data overlaps with the learning data. For example, the etching amount distribution is the knapsack in the knapsack problem, and the learning data are the items in the knapsack problem. Then, the number of times that the learning data overlaps with the learning data is optimized so that the difference between the overlapped etching amount distribution and the target etching amount distribution in St110 is minimized. In other words, the etching amount distribution during etching of the first surface Wa in St13 is optimized.

[0079] Next, the etching conditions corresponding to the learning data optimized in St111 are integrated to determine the optimal etching conditions (St112 in FIG. 7). Specifically, the optimal etching conditions are determined by integrating the selected etching conditions so that the selected etching conditions are performed with an optimized number of overlaps. In other words, the optimal etching conditions that optimize the etching amount distribution are determined.

[0080] As described above, the optimal etching conditions for the first surface Wa are determined in St 12. In this case, by etching the first surface Wa of the wafer W under the optimal etching conditions in St 13, the etching amount distribution can be optimized and the first surface Wa can be processed into the target shape.

[0081] In determining the above-described optimum etching conditions, a target etching amount distribution can be obtained using estimated data, which is a high-dimensional thickness distribution with higher estimation accuracy based on actual measurement data at the optimum thickness measurement positions according to the first to third embodiments described below. Based on this target etching amount distribution, more optimized optimum etching conditions can be determined.

[0082] The optimal etching conditions for the first surface Wa determined in St12 are stored in the control device 150, and a history of the etching conditions is maintained in the control device 150. At this time, the learning data used to determine the optimal etching conditions is also stored. Similarly, the optimal etching conditions (and learning data) for the second surface Wb determined in St8 are also stored in the control device 150, and a history of the etching conditions is maintained in the control device 150.

[0083] As described above, the etching of the second surface Wb in St9 and the etching of the first surface Wa in St13 may be performed under predetermined etching conditions rather than the optimal etching conditions. For this reason, when setting the etching conditions, the user may be allowed to select whether or not to use learning data.

[0084] In the above wafer processing method, the etching amount distribution is used as learning data for controlling the etching process of the wafer W, but the etching amount deviation distribution may also be used. The etching amount deviation distribution is a distribution of values ​​obtained by subtracting the average value of the etching amount from the etching amount within the wafer surface. In such a case, when determining the optimal etching conditions in St8 and St12, the etching amount deviation distribution is used instead of the etching amount distribution. The etching amount deviation distribution is also used when determining the grinding target thickness distribution in St1.

[0085] (First Embodiment) <Bayesian Optimization> Next, a method for determining an optimal thickness measurement position for a wafer W according to the first embodiment will be described. In the first embodiment, an optimal thickness measurement position is determined by Bayesian optimization such that the estimated data calculated in St7, St11, or St14 described above is close to the true high-dimensional thickness distribution. The optimal thickness measurement position to be determined by the method according to this embodiment is referred to as a "Bayesian optimal position." Note that any known method can be used to calculate estimated data from actual measurement data. Note that, for convenience, the following description will be directed to a case where the Bayesian optimal position used in St7 or St11 is determined.

[0086] In the Bayesian optimum position determination method according to the first embodiment, first, data on high-dimensional thickness distribution in the radial direction of the wafer W after grinding in each of the grinding units 100 and 110 (hereinafter referred to as "training data") is accumulated (St201 in FIG. 8). Specifically, in St201, grinding and thickness measurement of a plurality of wafers W are repeated in each of the grinding units 100 and 110. More specifically, for the first grinding unit 100, the following steps are repeated: determining the grinding target thickness distribution of the first surface Wa of the wafer W (St1), grinding the first surface Wa (St2), cleaning the first surface Wa (St3), and measuring the thickness of the wafer W (St7). Furthermore, for the second grinding unit 110, determination of the grinding target thickness distribution of the second surfaces Wb of the plurality of wafers W (St1), grinding of the second surfaces Wb (St5), cleaning of the second surfaces Wb (St6), and thickness measurement of the wafers W (St11) are repeated. Note that in St201, a dummy wafer may be used as the wafer W, and grinding and thickness measurement may be performed on one side in each of the grinding units 100 and 110. In this case, grinding and thickness measurement may be performed on any one side without distinguishing between the first surfaces Wa and the second surfaces Wb.

[0087] By performing grinding and thickness measurement of the wafer W for each grinding unit 100, 110, multiple pieces of training data are acquired and accumulated for each grinding unit 100, 110. The training data is acquired, for example, in St7 or St11 of the above repetition, by measuring the radial thickness of the wafer W at thickness measurement positions that are greater than the number of Bayes' optimal positions using the thickness measurement devices 50, 71. In other words, the training data is higher-dimensional thickness distribution data than the actual measurement data acquired by measuring the thickness at the Bayes' optimal positions.

[0088] Next, based on the training data accumulated for each grinding unit 100, 110, a Bayesian optimal position is determined for each grinding unit 100, 110 by Bayesian optimization (Step 202 in FIG. 8). In Bayesian optimization, the point where the characteristic value in the acquisition function is maximum is sequentially determined as the thickness measurement position. In other words, the Bayesian optimal position determined in this manner is a thickness measurement position where, when estimated data is calculated from actual measurement data that would be obtained if the position were not measured, the error between the estimated data and the true high-dimensional thickness distribution is predicted to be large. In other words, by measuring the Bayesian optimal position, the error between the estimated data and the true high-dimensional thickness distribution can be reduced.

[0089] In conventional thickness measurement methods, thickness measurement positions are sometimes set at equally spaced positions in the radial direction of the wafer W, or sometimes determined arbitrarily by the user based on experience. In these cases, thickness measurement positions may be selected that result in a large error between the estimated data and the true high-dimensional thickness distribution. In contrast, the method according to the first embodiment can determine Bayesian optimal positions that reduce the error between the estimated data and the true high-dimensional thickness distribution, thereby improving estimation accuracy compared to conventional methods. In other words, when estimated data is calculated using a desired known method from actual measurement data measured at the Bayesian optimal positions, the estimated data can be made closer to the true high-dimensional thickness distribution.

[0090] Furthermore, by acquiring training data and performing Bayesian optimization for each grinding unit 100, 110, it is possible to determine a Bayesian optimal position for each grinding unit 100, 110. This allows thickness measurements to be performed at positions according to the grinding habits (tendencies) of each grinding unit 100, 110, thereby improving estimation accuracy.

[0091] While the above describes the case where the Bayesian optimal position to be used in St7 or St11 is determined, the method according to this embodiment can also determine the Bayesian optimal position to be used in St14. In this case, in St201, training data is accumulated by repeating the wafer processing method including St1 to St14 for the entire wafer processing system 1. That is, in this case, the training data in St201 is acquired not for each grinding unit 100, 110, but for the entire wafer processing system 1. Similarly, the Bayesian optimal position in St202 is determined for the entire wafer processing system 1. Even in this case, the estimation accuracy can be improved compared to conventional methods.

[0092] Second Embodiment <Sparse Modeling> Next, a method for determining an optimal thickness measurement position of a wafer W according to a second embodiment and a method for calculating estimated data from actual measurement data obtained by measuring the thickness at the optimal thickness measurement position will be described. In the second embodiment, an optimal thickness measurement position is determined by sparse modeling so that estimated data approximates a true high-dimensional thickness distribution. The optimal thickness measurement position to be determined is referred to as a "sparse sensor position." Furthermore, in the second embodiment, a high-dimensional transformation matrix for calculating estimated data is determined from actual measurement data acquired by measurement at the sparse sensor position. For convenience, the following description will be directed to a case where the sparse sensor position and high-dimensional transformation matrix used in St7 or St11 are determined.

[0093] In this determination method, first, training data in the radial direction of the wafer W after grinding in each of the grinding units 100 and 110 is accumulated (Step 301 in FIG. 9 ). Step 301 can be performed in the same manner as Step 201 in the first embodiment. In this case, the training data is acquired by measuring the radial thickness of the wafer W using the thickness measurement device 50 or 71 at thickness measurement positions that are greater than the number of sparse sensor positions described below, for example, in Step 7 or Step 11 of the above repetition. In other words, the training data is data of a higher-dimensional thickness distribution than the actual measurement data acquired by measuring the thickness at the sparse sensor positions.

[0094] Next, learning is performed based on the training data accumulated for each grinding unit 100, 110, and sparse sensor positions and high-dimensional transformation matrices are determined for each grinding unit 100, 110. Specifically, the sparse sensor positions and high-dimensional transformation matrices are determined by sparse modeling using convex optimization.

[0095] More specifically, any training data z (z∈R) acquired by measuring n measurement points in Step 301 that satisfies the following formula (1) is ｎ ), low-dimensional data x (x∈R ｒ ), and the sparsification matrix Ur (Ur∈R ｎ×ｒ ) Consider.

[0096] Also, a sparse measurement matrix H(H∈R) that gives p sparse sensor positions is defined, satisfying the following equations (2) and (3). ｐ×ｎ ), and virtual measurement data y (y∈R ｐ ) is considered. In this embodiment, the number p of sparse sensor positions is a predetermined number.

[0097] At this time, by sparse modeling using convex optimization, the sparsifying matrix Ur, the low-dimensional data x, and the sparse measurement matrix H that satisfy the formulas (1) to (3) are determined under constraints described below (Step 302 in FIG. 9). As a convex optimization technique, for example, the alternating direction method of multipliers (ADMM) can be used.

[0098] Furthermore, a high-dimensional transformation matrix A (A∈R) is calculated from the sparsification matrix Ur, the low-dimensional data x, and the sparse measurement matrix H determined above. ｎ×ｒ ) is calculated (Step 303 in FIG. 9). The high-dimensional transformation matrix A is expressed by the following equation (4).

[0099] According to the above method, it is possible to determine a sparse measurement matrix H and a high-dimensional transformation matrix A that give sparse sensor positions.

[0100] In the above wafer processing method, in St7 or St11, estimated data (z-hat) can be calculated from actual measurement data (y-hat) obtained by measuring the thickness at the sparse sensor position using the high-dimensional transformation matrix A according to the following equation (5).

[0101] In the above method, it is possible to determine the sparse sensor positions to be determined and the estimated data to be calculated using the high-dimensional transformation matrix A under constraints. In one embodiment, the constraints are determined (Step 310 in FIG. 9 ) prior to determining the sparse sensor positions and the high-dimensional transformation matrix A. Examples of the constraints include the number of sparse sensor positions, the specific radial positions of any sparse sensor positions, the number of samples in the training data, and the allowable error in the estimated data.

[0102] In one embodiment, the determination method further sets a constraint that "the sparse sensor positions to be determined include a predetermined thickness measurement position B, and the thickness of the wafer W measured at the thickness measurement position B is approximately equal to the thickness of the wafer W at the thickness measurement position B of the estimated data to be calculated." Note that "approximately equal" includes the difference between the thicknesses being equal to or less than a desired threshold. In this case, convex optimization is further performed on the high-dimensional transformation matrix A determined above using an alternating method (Step 311 in FIG. 9 ). This results in a high-dimensional transformation matrix A that satisfies the constraint. The constraint is preferably set when the estimation accuracy at a certain thickness measurement position B is more important than at other thickness measurement positions or when it is known that the estimation accuracy at the certain thickness measurement position B is worse than at other thickness measurement positions. This improves the estimation accuracy at the thickness measurement position B.

[0103] According to the sparse sensor positions determined by the method of the second embodiment, when estimated data is calculated from actual measurement data measured at the sparse sensor positions using the high-dimensional transformation matrix A, the estimated data can be made closer to the true high-dimensional thickness distribution. As a result, even if the number of thickness measurement positions is the same, the estimation accuracy is improved compared to the conventional case where the thickness measurement positions are arbitrarily determined by the user.

[0104] Furthermore, it has been found that the estimation accuracy improves to a certain extent as the number of training data used in learning St302 increases. The inventors conducted verification and compared estimated data according to examples using different numbers of training data for learning with estimated data according to a comparative example in which the user arbitrarily determines the thickness measurement position as in the conventional method. The comparison was performed on the mean absolute error and maximum absolute error between the estimated data and the true high-dimensional thickness distribution. In this case, the example trained with 16 training data sheets achieved a lower mean absolute error than the comparative example. Furthermore, the example trained with 11 training data sheets achieved a lower maximum absolute error than the comparative example.

[0105] Furthermore, the inventors conducted verification and found that when a constraint to reduce the number of thickness measurement positions is set, the estimation accuracy is significantly improved compared to the conventional method in which the thickness measurement positions are arbitrarily determined by the user, even if the amount of training data used for learning is small. In this regard, for example, by repeatedly performing the above method while reducing the number p of sparse sensor positions, a smaller number p of sparse sensor positions may be determined so that the estimation accuracy does not fall below a desired threshold in learning using a certain amount of training data.

[0106] According to the method of the second embodiment, the sparse sensor positions and the high-dimensional transformation matrix A are simultaneously optimized, so that the estimation accuracy can be improved even with a smaller number of sparse sensor positions. Furthermore, even when the number of sparse sensor positions is smaller, the estimation accuracy can be improved by ensuring a sufficient number of training data used for learning.

[0107] Furthermore, by accumulating and learning training data for each of the grinding units 100 and 110, it is possible to determine the sparse sensor position and the high-dimensional transformation matrix A for each of the grinding units 100 and 110. This allows thickness measurements to be performed at positions according to the grinding habits (tendencies) of each of the grinding units 100 and 110, thereby improving estimation accuracy.

[0108] Furthermore, the estimated data calculated using the high-dimensional transformation matrix A does not necessarily pass through the sparse sensor position. In other words, a sparse sensor position and a high-dimensional transformation matrix A can be determined that do not pass through the sparse sensor position but provide higher estimation accuracy. Constraints can also be set so that a sparse sensor position and a high-dimensional transformation matrix A that do not pass through the sparse sensor position are determined. This makes it possible to determine a sparse sensor position and a high-dimensional transformation matrix A that enable calculation of estimated data that is more robust against noise.

[0109] Furthermore, the high-dimensional transformation matrix A determined by the above method includes information corresponding to the grinding habits (tendencies) of each of the grinding units 100 and 110. Based on this information, for example, in the grinding units 100 and 110, the relative tilt of the chucks 93 a and 93 b may be adjusted using the tilt adjustment mechanism 95.

[0110] While the above describes the case where the sparse sensor positions and high-dimensional transformation matrix A used in St7 or St11 are determined, the method according to this embodiment can also determine the sparse sensor positions and high-dimensional transformation matrix A used in St14. In this case, in St301, training data is accumulated by repeating the wafer processing method including St1 to St14 for the entire wafer processing system 1. That is, in this case, the training data in St301 is acquired not for each grinding unit 100, 110, but for the entire wafer processing system 1. Similarly, the sparse sensor positions and high-dimensional transformation matrix A in St302 and St303 are also determined for the entire wafer processing system 1. Even in this case, the estimation accuracy can be improved compared to conventional methods.

[0111] (Modification of Second Embodiment) In the second embodiment, the sparsification matrix Ur is calculated using singular value decomposition of the training data z expressed in the above formula (1). However, this is not limited to this, and the following modification is also possible. In this modification, a wavelet transform matrix is ​​used instead of the sparsification matrix Ur expressed in the above formula (1). That is, in the above formulas (3) and (4), the high-dimensional transformation matrix A is determined using a wavelet transform matrix instead of the sparsification matrix Ur. In this case, since the wavelet transform matrix is ​​known, the step of St301 of accumulating training data can be omitted. Note that a small amount of training data may be acquired in St301, and the training data may be used to verify the estimation accuracy of the estimated data using the high-dimensional transformation matrix A. According to this modification, it is possible to determine an optimal thickness measurement position by wavelet transform so that the estimated data approximates the true high-dimensional thickness distribution.

[0112] The embodiments disclosed herein should be considered to be illustrative in all respects and not restrictive. The above-described embodiments may be omitted, substituted, or modified in various ways without departing from the scope and spirit of the appended claims. For example, the components of the above-described embodiments may be arbitrarily combined. Such an arbitrary combination naturally provides the functions and effects of each of the components involved in the combination, and also provides other functions and effects that are apparent to those skilled in the art from the description of this specification.

[0113] In the above embodiment, the thickness distribution of the wafer W after grinding or etching is measured by the thickness measuring devices 50 and 71, and the estimated data is calculated, but the present disclosure is not limited to such an example. That is, the technology disclosed herein can be applied to measuring the thickness distribution of the wafer W after a desired process in which the thickness distribution fluctuates.

[0114] In the above embodiment, the training data is obtained using the thickness measurement devices 50 and 71, but the present invention is not limited to this example. That is, the training data may be obtained by measuring the thickness of the wafers W processed in the grinding units 100 and 110 using another thickness measurement device provided outside the wafer processing system 1.

[0115] In the above embodiment, the acquisition of training data is described as being performed in St201 or St301 independently of the wafer processing method for the production processing of wafers W, but this is not limited to this example. That is, among the wafers W processed in the wafer processing method as the actual production processing, some wafers W may be extracted and their high-dimensional thickness distribution may be measured, thereby acquiring or updating training data in parallel with the wafer processing method. These some wafers W may be dummy wafers.

[0116] Furthermore, the effects described herein are merely descriptive or exemplary and are not limiting. In other words, the technology according to the present disclosure may achieve other effects that are apparent to those skilled in the art from the description of this specification, in addition to or in place of the above-described effects.

[0117] 1 wafer processing system 90 grinding device 150 control device W wafer

Claims

1. A method for determining an optimal thickness measurement position when measuring the thickness distribution of a substrate processed in a substrate processing apparatus, comprising determining the optimal thickness measurement position based on training data, wherein the training data is obtained in advance by measuring the high-dimensional thickness distribution of one or more of the processed substrates, and the optimal thickness measurement position to be determined is a thickness measurement position optimized based on the training data so that when estimated data, which is a high-dimensional thickness distribution, is calculated based on actual measurement data obtained by measuring the thickness of the substrate at a certain thickness measurement position, the estimated data will be close to the true high-dimensional thickness distribution.

2. The method for determining an optimal thickness measurement position according to claim 1, wherein the substrate processing apparatus comprises a plurality of grinding units configured to process the substrate by grinding, the training data is obtained in advance for each grinding unit by measuring the thickness of the substrate processed for each grinding unit, and in determining the optimal thickness measurement position, the optimal thickness measurement position is determined for each grinding unit based on the training data for each grinding unit.

3. A method for determining an optimal thickness measurement position according to claim 1 or 2, wherein in determining the optimal thickness measurement position, the optimal thickness measurement position is determined by Bayesian optimization based on the training data.

4. A method for determining an optimal thickness measurement position according to claim 1 or 2, wherein a plurality of sets of training data are acquired in advance, and determining the optimal thickness measurement position comprises determining the optimal thickness measurement position by sparse modeling using convex optimization based on the plurality of sets of training data, and further comprising determining a high-dimensional transformation matrix for calculating the estimated data from the actual measurement data obtained by measuring the thickness of the substrate at the optimal thickness measurement position.

5. A method for determining an optimal thickness measurement position as described in claim 4, wherein, in determining the optimal thickness measurement position, the sparse modeling is performed while imposing predetermined constraints, and the constraints include the constraint that the optimal thickness measurement position to be determined includes one or more predetermined specific thickness measurement positions, and the difference between the thickness of the substrate at the thickness measurement position and the thickness of the substrate at the thickness measurement position of the estimated data to be calculated is equal to or less than a threshold.

6. A substrate processing method for processing substrates in a substrate processing apparatus, comprising: processing the substrate by grinding; measuring the thickness distribution of the processed substrate at a predetermined optimum thickness measurement position to obtain actual measurement data; and calculating estimated data, which is a high-dimensional thickness distribution, from the actual measurement data, wherein the optimum thickness measurement position is predetermined by a method including: measuring the thickness distribution of one or more processed substrates to obtain one or more training data, which are high-dimensional thickness distributions of the substrates, and determining the optimum thickness measurement position based on the training data, and the optimum thickness measurement position is a thickness measurement position optimized based on the training data so that when the estimated data is calculated based on the actual measurement data obtained by measuring the thickness of the substrate at a certain thickness measurement position, the estimated data will be close to the true high-dimensional thickness distribution.

7. The substrate processing method of claim 6, wherein the substrate processing apparatus comprises: one or more grinding units configured to process the substrates by grinding them; and a thickness measurement unit configured to measure the thickness distribution of the processed substrates at predetermined optimum thickness measurement positions, wherein the optimum thickness measurement positions are determined in advance by: acquiring the training data by measuring the thickness of the substrates processed for each grinding unit with the thickness measurement device, thereby acquiring the training data for each grinding unit; determining the optimum thickness measurement positions by determining the optimum thickness measurement positions for each grinding unit based on the training data for each grinding unit; and acquiring the actual measurement data by measuring the thickness distribution of the processed substrates at the optimum thickness measurement positions predetermined for each grinding unit.

8. A substrate processing method as described in claim 6 or 7, wherein the optimal thickness measurement position is determined in advance by determining the optimal thickness measurement position using Bayesian optimization based on the training data in determining the optimal thickness measurement position.

9. The substrate processing method of claim 6 or 7, wherein the optimal thickness measurement position is predetermined by: acquiring a plurality of training data in acquiring the training data; determining the optimal thickness measurement position by sparse modeling using convex optimization based on the plurality of training data in determining the optimal thickness measurement position; and calculating the estimated data by using a high-dimensional transformation matrix predetermined by the sparse modeling to calculate the estimated data from the actual measurement data obtained by measuring the thickness of the substrate at the optimal thickness measurement position.

10. The substrate processing method of claim 9, wherein, in determining the optimal thickness measurement position, the sparse modeling is performed while imposing predetermined constraints, and the constraints include a constraint that the optimal thickness measurement position to be determined includes one or more predetermined specific thickness measurement positions, and a difference between the thickness of the substrate at the thickness measurement position and the thickness of the substrate at the thickness measurement position of the estimated data to be calculated is equal to or less than a threshold value.

11. A substrate processing apparatus for processing substrates, comprising: a grinding unit configured to process the substrate by grinding; a thickness measurement unit configured to measure a thickness distribution of the processed substrate at a predetermined optimum thickness measurement position; and a control unit, wherein the control unit executes control including: processing the substrate by grinding; measuring the thickness distribution of the processed substrate at the optimum thickness measurement position to obtain actual measurement data; and calculating estimated data, which is a high-dimensional thickness distribution, from the actual measurement data, wherein the optimum thickness measurement position is predetermined by a method including: measuring the thickness distribution of one or more processed substrates to obtain one or more training data, which are high-dimensional thickness distributions of the substrates, and determining the optimum thickness measurement position based on the training data, and the optimum thickness measurement position is a thickness measurement position optimized based on the training data so that when the estimated data is calculated based on the actual measurement data obtained by measuring the thickness of the substrate at a certain thickness measurement position, the estimated data will be close to a true high-dimensional thickness distribution.

Images